PROPAGATION CONSTANT OF A T-NETWORK

A symmetrical T network terminated by its characteristic impedance Z0T is shown in Fig. a

FIG. Symmetrical network terminated in ZOT

By KVL in the right-hand mesh

Z2(I1–I2)–Z1/2 I2 – ZOTI2 = 0

Z2I1 = (Z1/2+ZOT+Z2)I2

I1/I2 = 1/Z2(Z1/2+ZOT+Z2)

Also, I1/I2 = eY

Or eY = 1/Z2(Z1/2+ZOT+Z2)

ZOT = Z2(eY–1)–Z1/2

The characteristic impedance of a symmetrical T network is given by

ZOT = √Z1Z2(1+Z1/4Z2)

Z2(eY–1)–Z1/2=√Z1Z2(1+Z1/4Z3)

[Z2(eY–1)–Z1/2]2 = Z1Z2 + Z21/4

Z22(ey–1)2 + Z21/4 – Z1Z2(ey–1) = Z1Z2 + Z21/4

Z22(ey–1)2 = Z1Z2eY

e2Y – 2eY + 1 = Z1/Z2eY

eY – 2 + e–y = 1 + Z1/2Z2

coshy = 1 + Z1/2Z2

Also cos hy = 1 + 2 sin h2 y/2

1+2 sin h2 y/2 = 1 + Z1/2Z2

sin h y/2 = √Z1/4Z2

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